Abstract:
The solution operator of PDEs generates infinite-dimensional dynamical
systems. However, numerical algorithms approximating the solutions are
inherently finite dimensional. Work suggesting numerical schemes can
capture the correct dynamics of the infinite-dimensional systems they
approximate, provided the space and time mesh are
sufficiently refined, will be presented. The theory is applied to the
Navier-Stokes equations, and estimates on the resolution required of the
numerical scheme are also given.